A Simple Framework for Contrastive Learning of Visual Representations

Introduction

Learning effective visual representations without human supervision is a long-standing problem. Most mainstream approaches fall into one of two classes: generative or discriminative. Generative approaches learn to generate or otherwise model pixels in the input space (Hinton et al., 2006; Kingma & Welling, 2013; Goodfellow et al., 2014). However, pixel-level generation is computationally expensive and may not be necessary for representation learning. Discriminative approaches learn representations using objective functions similar to those used for supervised learning, but train networks to perform pretext tasks where both the inputs and labels are derived from an unlabeled dataset. Many such approaches have relied on heuristics to design pretext tasks (Doersch et al., 2015; Zhang et al., 2016; Noroozi & Favaro, 2016; Gidaris et al., 2018), which could limit the generality of the learned representations. Discriminative approaches based on contrastive learning in the latent space have recently shown great promise, achieving state-of-the-art results (Hadsell et al., 2006; Dosovitskiy et al., 2014; Oord et al., 2018; Bachman et al., 2019).

In this work, we introduce a simple framework for contrastive learning of visual representations, which we call SimCLR. Not only does SimCLR outperform previous work (Figure 1), but it is also simpler, requiring neither specialized architectures (Bachman et al., 2019; Hénaff et al., 2019) nor a memory bank (Wu et al., 2018; Tian et al., 2019; He et al., 2019; Misra & van der Maaten, 2019).

In order to understand what enables good contrastive representation learning, we systematically study the major components of our framework and show that:

Composition of multiple data augmentation operations is crucial in defining the contrastive prediction tasks that yield effective representations. In addition, unsupervised contrastive learning benefits from stronger data augmentation than supervised learning.

Introducing a learnable nonlinear transformation between the representation and the contrastive loss substantially improves the quality of the learned representations.

Representation learning with contrastive cross entropy loss benefits from normalized embeddings and an appropriately adjusted temperature parameter.

Contrastive learning benefits from larger batch sizes and longer training compared to its supervised counterpart. Like supervised learning, contrastive learning benefits from deeper and wider networks.

We combine these findings to achieve a new state-of-the-art in self-supervised and semi-supervised learning on ImageNet ILSVRC-2012 (Russakovsky et al., 2015). Under the linear evaluation protocol, SimCLR achieves 76.5% top-1 accuracy, which is a 7% relative improvement over previous state-of-the-art (Hénaff et al., 2019). When fine-tuned with only 1% of the ImageNet labels, SimCLR achieves 85.8% top-5 accuracy, a relative improvement of 10% (Hénaff et al., 2019). When fine-tuned on other natural image classification datasets, SimCLR performs on par with or better than a strong supervised baseline (Kornblith et al., 2019) on 10 out of 12 datasets.

Method

Inspired by recent contrastive learning algorithms (see Section 7 for an overview), SimCLR learns representations by maximizing agreement between differently augmented views of the same data example via a contrastive loss in the latent space. As illustrated in Figure 2, this framework comprises the following four major components.

A small neural network projection head $g(\cdot)$ that maps representations to the space where contrastive loss is applied. We use a MLP with one hidden layer to obtain $\bm{z}_{i}=g(\bm{h}_{i})=W^{(2)}\sigma(W^{(1)}\bm{h}_{i})$ where $\sigma$ is a ReLU non-linearity. As shown in section 4, we find it beneficial to define the contrastive loss on $\bm{z}_{i}$’s rather than $\bm{h}_{i}$’s.

Algorithm 1 summarizes the proposed method.

2 Training with Large Batch Size

To keep it simple, we do not train the model with a memory bank (Wu et al., 2018; He et al., 2019). Instead, we vary the training batch size $N$ from 256 to 8192. A batch size of 8192 gives us 16382 negative examples per positive pair from both augmentation views. Training with large batch size may be unstable when using standard SGD/Momentum with linear learning rate scaling (Goyal et al., 2017). To stabilize the training, we use the LARS optimizer (You et al., 2017) for all batch sizes. We train our model with Cloud TPUs, using 32 to 128 cores depending on the batch size.With 128 TPU v3 cores, it takes $\sim$1.5 hours to train our ResNet-50 with a batch size of 4096 for 100 epochs.

Global BN. Standard ResNets use batch normalization (Ioffe & Szegedy, 2015). In distributed training with data parallelism, the BN mean and variance are typically aggregated locally per device. In our contrastive learning, as positive pairs are computed in the same device, the model can exploit the local information leakage to improve prediction accuracy without improving representations. We address this issue by aggregating BN mean and variance over all devices during the training. Other approaches include shuffling data examples across devices (He et al., 2019), or replacing BN with layer norm (Hénaff et al., 2019).

3 Evaluation Protocol

Here we lay out the protocol for our empirical studies, which aim to understand different design choices in our framework.

Dataset and Metrics. Most of our study for unsupervised pretraining (learning encoder network $f$ without labels) is done using the ImageNet ILSVRC-2012 dataset (Russakovsky et al., 2015). Some additional pretraining experiments on CIFAR-10 (Krizhevsky & Hinton, 2009) can be found in Appendix B.9. We also test the pretrained results on a wide range of datasets for transfer learning. To evaluate the learned representations, we follow the widely used linear evaluation protocol (Zhang et al., 2016; Oord et al., 2018; Bachman et al., 2019; Kolesnikov et al., 2019), where a linear classifier is trained on top of the frozen base network, and test accuracy is used as a proxy for representation quality. Beyond linear evaluation, we also compare against state-of-the-art on semi-supervised and transfer learning.

Data Augmentation for Contrastive Representation Learning

Data augmentation defines predictive tasks. While data augmentation has been widely used in both supervised and unsupervised representation learning (Krizhevsky et al., 2012; Hénaff et al., 2019; Bachman et al., 2019), it has not been considered as a systematic way to define the contrastive prediction task. Many existing approaches define contrastive prediction tasks by changing the architecture. For example, Hjelm et al. (2018); Bachman et al. (2019) achieve global-to-local view prediction via constraining the receptive field in the network architecture, whereas Oord et al. (2018); Hénaff et al. (2019) achieve neighboring view prediction via a fixed image splitting procedure and a context aggregation network. We show that this complexity can be avoided by performing simple random cropping (with resizing) of target images, which creates a family of predictive tasks subsuming the above mentioned two, as shown in Figure 3. This simple design choice conveniently decouples the predictive task from other components such as the neural network architecture. Broader contrastive prediction tasks can be defined by extending the family of augmentations and composing them stochastically.

To systematically study the impact of data augmentation, we consider several common augmentations here. One type of augmentation involves spatial/geometric transformation of data, such as cropping and resizing (with horizontal flipping), rotation (Gidaris et al., 2018) and cutout (DeVries & Taylor, 2017). The other type of augmentation involves appearance transformation, such as color distortion (including color dropping, brightness, contrast, saturation, hue) (Howard, 2013; Szegedy et al., 2015), Gaussian blur, and Sobel filtering. Figure 4 visualizes the augmentations that we study in this work.

To understand the effects of individual data augmentations and the importance of augmentation composition, we investigate the performance of our framework when applying augmentations individually or in pairs. Since ImageNet images are of different sizes, we always apply crop and resize images (Krizhevsky et al., 2012; Szegedy et al., 2015), which makes it difficult to study other augmentations in the absence of cropping. To eliminate this confound, we consider an asymmetric data transformation setting for this ablation. Specifically, we always first randomly crop images and resize them to the same resolution, and we then apply the targeted transformation(s) only to one branch of the framework in Figure 2, while leaving the other branch as the identity (i.e. $t(\bm{x}_{i})=\bm{x}_{i}$). Note that this asymmetric data augmentation hurts the performance. Nonetheless, this setup should not substantively change the impact of individual data augmentations or their compositions.

Figure 5 shows linear evaluation results under individual and composition of transformations. We observe that no single transformation suffices to learn good representations, even though the model can almost perfectly identify the positive pairs in the contrastive task. When composing augmentations, the contrastive prediction task becomes harder, but the quality of representation improves dramatically. Appendix B.2 provides a further study on composing broader set of augmentations.

One composition of augmentations stands out: random cropping and random color distortion. We conjecture that one serious issue when using only random cropping as data augmentation is that most patches from an image share a similar color distribution. Figure 6 shows that color histograms alone suffice to distinguish images. Neural nets may exploit this shortcut to solve the predictive task. Therefore, it is critical to compose cropping with color distortion in order to learn generalizable features.

2 Contrastive learning needs stronger data augmentation than supervised learning

To further demonstrate the importance of the color augmentation, we adjust the strength of color augmentation as shown in Table 1. Stronger color augmentation substantially improves the linear evaluation of the learned unsupervised models. In this context, AutoAugment (Cubuk et al., 2019), a sophisticated augmentation policy found using supervised learning, does not work better than simple cropping + (stronger) color distortion. When training supervised models with the same set of augmentations, we observe that stronger color augmentation does not improve or even hurts their performance. Thus, our experiments show that unsupervised contrastive learning benefits from stronger (color) data augmentation than supervised learning. Although previous work has reported that data augmentation is useful for self-supervised learning (Doersch et al., 2015; Bachman et al., 2019; Hénaff et al., 2019; Asano et al., 2019), we show that data augmentation that does not yield accuracy benefits for supervised learning can still help considerably with contrastive learning.

Architectures for Encoder and Head

Figure 7 shows, perhaps unsurprisingly, that increasing depth and width both improve performance. While similar findings hold for supervised learning (He et al., 2016), we find the gap between supervised models and linear classifiers trained on unsupervised models shrinks as the model size increases, suggesting that unsupervised learning benefits more from bigger models than its supervised counterpart.

2 A nonlinear projection head improves the representation quality of the layer before it

We then study the importance of including a projection head, i.e. $g(\bm{h})$. Figure 8 shows linear evaluation results using three different architecture for the head: (1) identity mapping; (2) linear projection, as used by several previous approaches (Wu et al., 2018); and (3) the default nonlinear projection with one additional hidden layer (and ReLU activation), similar to Bachman et al. (2019). We observe that a nonlinear projection is better than a linear projection (+3%), and much better than no projection (>10%). When a projection head is used, similar results are observed regardless of output dimension. Furthermore, even when nonlinear projection is used, the layer before the projection head, $\bm{h}$, is still much better (>10%) than the layer after, $\bm{z}=g(\bm{h})$, which shows that the hidden layer before the projection head is a better representation than the layer after.

We conjecture that the importance of using the representation before the nonlinear projection is due to loss of information induced by the contrastive loss. In particular, $\bm{z}=g(\bm{h})$ is trained to be invariant to data transformation. Thus, $g$ can remove information that may be useful for the downstream task, such as the color or orientation of objects. By leveraging the nonlinear transformation $g(\cdot)$, more information can be formed and maintained in $\bm{h}$. To verify this hypothesis, we conduct experiments that use either $\bm{h}$ or $g(\bm{h})$ to learn to predict the transformation applied during the pretraining. Here we set $g(h)=W^{(2)}\sigma(W^{(1)}h)$, with the same input and output dimensionality (i.e. 2048). Table 3 shows $\bm{h}$ contains much more information about the transformation applied, while $g(\bm{h})$ loses information. Further analysis can be found in Appendix B.4.

Loss Functions and Batch Size

2 Contrastive learning benefits (more) from larger batch sizes and longer training

Figure 9 shows the impact of batch size when models are trained for different numbers of epochs. We find that, when the number of training epochs is small (e.g. 100 epochs), larger batch sizes have a significant advantage over the smaller ones. With more training steps/epochs, the gaps between different batch sizes decrease or disappear, provided the batches are randomly resampled. In contrast to supervised learning (Goyal et al., 2017), in contrastive learning, larger batch sizes provide more negative examples, facilitating convergence (i.e. taking fewer epochs and steps for a given accuracy). Training longer also provides more negative examples, improving the results. In Appendix B.1, results with even longer training steps are provided.

Comparison with State-of-the-art

In this subsection, similar to Kolesnikov et al. (2019); He et al. (2019), we use ResNet-50 in 3 different hidden layer widths (width multipliers of $1\times$, $2\times$, and $4\times$). For better convergence, our models here are trained for 1000 epochs.

Linear evaluation. Table 6 compares our results with previous approaches (Zhuang et al., 2019; He et al., 2019; Misra & van der Maaten, 2019; Hénaff et al., 2019; Kolesnikov et al., 2019; Donahue & Simonyan, 2019; Bachman et al., 2019; Tian et al., 2019) in the linear evaluation setting (see Appendix B.6). Table 1 shows more numerical comparisons among different methods. We are able to use standard networks to obtain substantially better results compared to previous methods that require specifically designed architectures. The best result obtained with our ResNet-50 ($4\times$) can match the supervised pretrained ResNet-50.

Semi-supervised learning. We follow Zhai et al. (2019) and sample 1% or 10% of the labeled ILSVRC-12 training datasets in a class-balanced way ($\sim$12.8 and $\sim$128 images per class respectively). The details of sampling and exact subsets can be found in https://www.tensorflow.org/datasets/catalog/imagenet2012_subset. We simply fine-tune the whole base network on the labeled data without regularization (see Appendix B.5). Table 7 shows the comparisons of our results against recent methods (Zhai et al., 2019; Xie et al., 2019; Sohn et al., 2020; Wu et al., 2018; Donahue & Simonyan, 2019; Misra & van der Maaten, 2019; Hénaff et al., 2019). The supervised baseline from (Zhai et al., 2019) is strong due to intensive search of hyper-parameters (including augmentation). Again, our approach significantly improves over state-of-the-art with both 1% and 10% of the labels. Interestingly, fine-tuning our pretrained ResNet-50 (2$\times,4\times$) on full ImageNet are also significantly better then training from scratch (up to 2%, see Appendix B.2).

Transfer learning. We evaluate transfer learning performance across 12 natural image datasets in both linear evaluation (fixed feature extractor) and fine-tuning settings. Following Kornblith et al. (2019), we perform hyperparameter tuning for each model-dataset combination and select the best hyperparameters on a validation set. Table 8 shows results with the ResNet-50 ($4\times$) model. When fine-tuned, our self-supervised model significantly outperforms the supervised baseline on 5 datasets, whereas the supervised baseline is superior on only 2 (i.e. Pets and Flowers). On the remaining 5 datasets, the models are statistically tied. Full experimental details as well as results with the standard ResNet-50 architecture are provided in Appendix B.8.

Related Work

The idea of making representations of an image agree with each other under small transformations dates back to Becker & Hinton (1992). We extend it by leveraging recent advances in data augmentation, network architecture and contrastive loss. A similar consistency idea, but for class label prediction, has been explored in other contexts such as semi-supervised learning (Xie et al., 2019; Berthelot et al., 2019).

Handcrafted pretext tasks. The recent renaissance of self-supervised learning began with artificially designed pretext tasks, such as relative patch prediction (Doersch et al., 2015), solving jigsaw puzzles (Noroozi & Favaro, 2016), colorization (Zhang et al., 2016) and rotation prediction (Gidaris et al., 2018; Chen et al., 2019). Although good results can be obtained with bigger networks and longer training (Kolesnikov et al., 2019), these pretext tasks rely on somewhat ad-hoc heuristics, which limits the generality of learned representations.

Contrastive visual representation learning. Dating back to Hadsell et al. (2006), these approaches learn representations by contrasting positive pairs against negative pairs. Along these lines, Dosovitskiy et al. (2014) proposes to treat each instance as a class represented by a feature vector (in a parametric form). Wu et al. (2018) proposes to use a memory bank to store the instance class representation vector, an approach adopted and extended in several recent papers (Zhuang et al., 2019; Tian et al., 2019; He et al., 2019; Misra & van der Maaten, 2019). Other work explores the use of in-batch samples for negative sampling instead of a memory bank (Doersch & Zisserman, 2017; Ye et al., 2019; Ji et al., 2019).

Recent literature has attempted to relate the success of their methods to maximization of mutual information between latent representations (Oord et al., 2018; Hénaff et al., 2019; Hjelm et al., 2018; Bachman et al., 2019). However, it is not clear if the success of contrastive approaches is determined by the mutual information, or by the specific form of the contrastive loss (Tschannen et al., 2019).

We note that almost all individual components of our framework have appeared in previous work, although the specific instantiations may be different. The superiority of our framework relative to previous work is not explained by any single design choice, but by their composition. We provide a comprehensive comparison of our design choices with those of previous work in Appendix C.

Conclusion

In this work, we present a simple framework and its instantiation for contrastive visual representation learning. We carefully study its components, and show the effects of different design choices. By combining our findings, we improve considerably over previous methods for self-supervised, semi-supervised, and transfer learning.

Our approach differs from standard supervised learning on ImageNet only in the choice of data augmentation, the use of a nonlinear head at the end of the network, and the loss function. The strength of this simple framework suggests that, despite a recent surge in interest, self-supervised learning remains undervalued.

Acknowledgements

We would like to thank Xiaohua Zhai, Rafael Müller and Yani Ioannou for their feedback on the draft. We are also grateful for general support from Google Research teams in Toronto and elsewhere.

References

Appendix A Data Augmentation Details

In our default pretraining setting (which is used to train our best models), we utilize random crop (with resize and random flip), random color distortion, and random Gaussian blur as the data augmentations. The details of these three augmentations are provided below.

Color distortion is composed by color jittering and color dropping. We find stronger color jittering usually helps, so we set a strength parameter.

A pseudo-code for color distortion using TensorFlow is as follows.

A pseudo-code for color distortion using Pytorch is as follows Our code and results are based on Tensorflow, the Pytorch code here is a reference..

This augmentation is in our default policy. We find it helpful, as it improves our ResNet-50 trained for 100 epochs from 63.2% to 64.5%. We blur the image 50% of the time using a Gaussian kernel. We randomly sample $\sigma\in[0.1,2.0]$, and the kernel size is set to be 10% of the image height/width.

Appendix B Additional Experimental Results

Figure B.2 shows the top-5 accuracy on linear evaluation when trained with different batch sizes and training epochs. The conclusion is very similar to top-1 accuracy shown before, except that the differences between different batch sizes and training steps seems slightly smaller here.

We also train with larger batch size (up to 32K) and longer (up to 3200 epochs), with the square root learning rate scaling. A shown in Figure B.2, the performance seems to saturate with a batch size of 8192, while training longer can still significantly improve the performance.

B.2 Broader composition of data augmentations further improves performance

Our best results in the main text (Table 6 and 7) can be further improved when expanding the default augmentation policy to include the following: (1) Sobel filtering, (2) additional color distortion (equalize, solarize), and (3) motion blur. For linear evaluation protocol, the ResNet-50 models ($1\times,2\times,4\times$) trained with broader data augmentations achieve 70.0 (+0.7), 74.4 (+0.2), 76.8 (+0.3), respectively.

Table B.2 shows ImageNet accuracy obtained by fine-tuning the SimCLR model (see Appendix B.5 for the details of fine-tuning procedure). Interestingly, when fine-tuned on full (100%) ImageNet training set, our ResNet (4$\times$) model achieves 80.4% top-1 / 95.4% top-5 It is 80.1% top-1 / 95.2% top-5 without broader augmentations for pretraining SimCLR., which is significantly better than that (78.4% top-1 / 94.2% top-5) of training from scratch using the same set of augmentations (i.e. random crop and horizontal flip). For ResNet-50 (2$\times$), fine-tuning our pre-trained ResNet-50 (2$\times$) is also better than training from scratch (77.8% top-1 / 93.9% top-5). There is no improvement from fine-tuning for ResNet-50.

B.3 Effects of Longer Training for Supervised Models

Here we perform experiments to see how training steps and stronger data augmentation affect supervised training. We test ResNet-50 and ResNet-50 (4$\times$) under the same set of data augmentations (random crops, color distortion, 50% Gaussian blur) as used in our unsupervised models. Figure B.3 shows the top-1 accuracy. We observe that there is no significant benefit from training supervised models longer on ImageNet. Stronger data augmentation slightly improves the accuracy of ResNet-50 (4$\times$) but does not help on ResNet-50. When stronger data augmentation is applied, ResNet-50 generally requires longer training (e.g. 500 epochs With AutoAugment (Cubuk et al., 2019), optimal test accuracy can be achieved between 900 and 500 epochs.) to obtain the optimal result, while ResNet-50 (4$\times$) does not benefit from longer training.

B.4 Understanding The Non-Linear Projection Head

Figure B.4 shows the eigenvalue distribution of linear projection matrix $W\in R^{2048\times 2048}$ used to compute $\bm{z}=W\bm{h}$. This matrix has relatively few large eigenvalues, indicating that it is approximately low-rank.

Figure B.4 shows t-SNE (Maaten & Hinton, 2008) visualizations of $\bm{h}$ and $\bm{z}=g(\bm{h})$ for randomly selected 10 classes by our best ResNet-50 (top-1 linear evaluation 69.3%). Classes represented by $\bm{h}$ are better separated compared to $\bm{z}$.

B.5 Semi-supervised Learning via Fine-Tuning

Table B.4 shows the comparisons of top-1 accuracy for different methods for semi-supervised learning. Our models significantly improve state-of-the-art.

B.6 Linear Evaluation

B.7 Correlation Between Linear Evaluation and Fine-Tuning

Here we study the correlation between linear evaluation and fine-tuning under different settings of training step and network architecture.

Figure B.5 shows linear evaluation versus fine-tuning when training epochs of a ResNet-50 (using batch size of 4096) are varied from 50 to 3200 as in Figure B.2. While they are almost linearly correlated, it seems fine-tuning on a small fraction of labels benefits more from training longer.

Figure B.6 shows shows linear evaluation versus fine-tuning for different architectures of choice.

B.8 Transfer Learning

We evaluated the performance of our self-supervised representation for transfer learning in two settings: linear evaluation, where a logistic regression classifier is trained to classify a new dataset based on the self-supervised representation learned on ImageNet, and fine-tuning, where we allow all weights to vary during training. In both cases, we follow the approach described by Kornblith et al. (2019), although our preprocessing differs slightly.

We investigated transfer learning performance on the Food-101 dataset (Bossard et al., 2014), CIFAR-10 and CIFAR-100 (Krizhevsky & Hinton, 2009), Birdsnap (Berg et al., 2014), the SUN397 scene dataset (Xiao et al., 2010), Stanford Cars (Krause et al., 2013), FGVC Aircraft (Maji et al., 2013), the PASCAL VOC 2007 classification task (Everingham et al., 2010), the Describable Textures Dataset (DTD) (Cimpoi et al., 2014), Oxford-IIIT Pets (Parkhi et al., 2012), Caltech-101 (Fei-Fei et al., 2004), and Oxford 102 Flowers (Nilsback & Zisserman, 2008). We follow the evaluation protocols in the papers introducing these datasets, i.e., we report top-1 accuracy for Food-101, CIFAR-10, CIFAR-100, Birdsnap, SUN397, Stanford Cars, and DTD; mean per-class accuracy for FGVC Aircraft, Oxford-IIIT Pets, Caltech-101, and Oxford 102 Flowers; and the 11-point mAP metric as defined in Everingham et al. (2010) for PASCAL VOC 2007. For DTD and SUN397, the dataset creators defined multiple train/test splits; we report results only for the first split. Caltech-101 defines no train/test split, so we randomly chose 30 images per class and test on the remainder, for fair comparison with previous work (Donahue et al., 2014; Simonyan & Zisserman, 2014).

We used the validation sets specified by the dataset creators to select hyperparameters for FGVC Aircraft, PASCAL VOC 2007, DTD, and Oxford 102 Flowers. For other datasets, we held out a subset of the training set for validation while performing hyperparameter tuning. After selecting the optimal hyperparameters on the validation set, we retrained the model using the selected parameters using all training and validation images. We report accuracy on the test set.

We fine-tuned the entire network using the weights of the pretrained network as initialization. We trained for 20,000 steps at a batch size of 256 using SGD with Nesterov momentum with a momentum parameter of 0.9. We set the momentum parameter for the batch normalization statistics to $\max(1-10/s,0.9)$ where $s$ is the number of steps per epoch. As data augmentation during fine-tuning, we performed only random crops with resize and flips; in contrast to pretraining, we did not perform color augmentation or blurring. At test time, we resized images to 256 pixels along the shorter side and took a $224\times 224$ center crop. (Additional accuracy improvements may be possible with further optimization of data augmentation, particularly on the CIFAR-10 and CIFAR-100 datasets.) We selected the learning rate and weight decay, with a grid of 7 logarithmically spaced learning rates between 0.0001 and 0.1 and 7 logarithmically spaced values of weight decay between $10^{-6}$ and $10^{-3}$, as well as no weight decay. We divide these values of weight decay by the learning rate.

We trained the network from random initialization using the same procedure as for fine-tuning, but for longer, and with an altered hyperparameter grid. We chose hyperparameters from a grid of 7 logarithmically spaced learning rates between 0.001 and 1.0 and 8 logarithmically spaced values of weight decay between $10^{-5}$ and $10^{-1.5}$. Importantly, our random initialization baselines are trained for 40,000 steps, which is sufficiently long to achieve near-maximal accuracy, as demonstrated in Figure 8 of Kornblith et al. (2019).

On Birdsnap, there are no statistically significant differences among methods, and on Food-101, Stanford Cars, and FGVC Aircraft datasets, fine-tuning provides only a small advantage over training from random initialization. However, on the remaining 8 datasets, pretraining has clear advantages.

We compare against architecturally identical ResNet models trained on ImageNet with standard cross-entropy loss. These models are trained with the same data augmentation as our self-supervised models (crops, strong color augmentation, and blur) and are also trained for 1000 epochs. We found that, although stronger data augmentation and longer training time do not benefit accuracy on ImageNet, these models performed significantly better than a supervised baseline trained for 90 epochs and ordinary data augmentation for linear evaluation on a subset of transfer datasets. The supervised ResNet-50 baseline achieves 76.3% top-1 accuracy on ImageNet, vs. 69.3% for the self-supervised counterpart, while the ResNet-50 ($4\times$) baseline achieves 78.3%, vs. 76.5% for the self-supervised model.

We test for the significance of differences between model with a permutation test. Given predictions of two models, we generate 100,000 samples from the null distribution by randomly exchanging predictions for each example and computing the difference in accuracy after performing this randomization. We then compute the percentage of samples from the null distribution that are more extreme than the observed difference in predictions. For top-1 accuracy, this procedure yields the same result as the exact McNemar test. The assumption of exchangeability under the null hypothesis is also valid for mean per-class accuracy, but not when computing average precision curves. Thus, we perform significance testing for a difference in accuracy on VOC 2007 rather than a difference in mAP. A caveat of this procedure is that it does not consider run-to-run variability when training the models, only variability arising from using a finite sample of images for evaluation.

B.8.2 Results with Standard ResNet

The ResNet-50 ($4\times$) results shown in Table 8 of the text show no clear advantage to the supervised or self-supervised models. With the narrower ResNet-50 architecture, however, supervised learning maintains a clear advantage over self-supervised learning. The supervised ResNet-50 model outperforms the self-supervised model on all datasets with linear evaluation, and most (10 of 12) datasets with fine-tuning. The weaker performance of the ResNet model compared to the ResNet ($4\times$) model may relate to the accuracy gap between the supervised and self-supervised models on ImageNet. The self-supervised ResNet gets 69.3% top-1 accuracy, 6.8% worse than the supervised model in absolute terms, whereas the self-supervised ResNet $(4\times)$ model gets 76.5%, which is only 1.8% worse than the supervised model.

B.9 CIFAR-10

While we focus on using ImageNet as the main dataset for pretraining our unsupervised model, our method also works with other datasets. We demonstrate it by testing on CIFAR-10 as follows.

As our goal is not to optimize CIFAR-10 performance, but rather to provide further confirmation of our observations on ImageNet, we use the same architecture (ResNet-50) for CIFAR-10 experiments. Because CIFAR-10 images are much smaller than ImageNet images, we replace the first 7x7 Conv of stride 2 with 3x3 Conv of stride 1, and also remove the first max pooling operation. For data augmentation, we use the same Inception crop (flip and resize to 32x32) as ImageNet,It is worth noting that, although CIFAR-10 images are much smaller than ImageNet images and image size does not differ among examples, cropping with resizing is still a very effective augmentation for contrastive learning. and color distortion (strength=0.5), leaving out Gaussian blur. We pretrain with learning rate in $\{0.5,1.0,1.5\}$, temperature in $\{0.1,0.5,1.0\}$, and batch size in $\{256,512,1024,2048,4096\}$. The rest of the settings (including optimizer, weight decay, etc.) are the same as our ImageNet training.

Our best model trained with batch size 1024 can achieve a linear evaluation accuracy of 94.0%, compared to 95.1% from the supervised baseline using the same architecture and batch size. The best self-supervised model that reports linear evaluation result on CIFAR-10 is AMDIM (Bachman et al., 2019), which achieves 91.2% with a model $25\times$ larger than ours. We note that our model can be improved by incorporating extra data augmentations as well as using a more suitable base network.

Figure B.7 shows the linear evaluation performance under different batch sizes and training steps. The results are consistent with our observations on ImageNet, although the largest batch size of 4096 seems to cause a small degradation in performance on CIFAR-10.

Figure B.8 shows the linear evaluation of model trained with three different temperatures under various batch sizes. We find that when training to convergence (e.g. training epochs > 300), the optimal temperature in $\{0.1,0.5,1.0\}$ is 0.5 and seems consistent regardless of the batch sizes. However, the performance with $\tau=0.1$ improves as batch size increases, which may suggest a small shift of optimal temperature towards 0.1.

B.10 Tuning For Other Loss Functions

The learning rate that works best for NT-Xent loss may not be a good learning rate for other loss functions. To ensure a fair comparison, we also tune hyperparameters for both margin loss and logistic loss. Specifically, we tune learning rate in $\{0.01,0.1,0.3,0.5,1.0\}$ for both loss functions. We further tune the margin in $\{0,0.4,0.8,1.6\}$ for margin loss, the temperature in $\{0.1,0.2,0.5,1.0\}$ for logistic loss. For simplicity, we only consider the negatives from one augmentation view (instead of both sides), which slightly impairs performance but ensures fair comparison.

Appendix C Further Comparison to Related Methods

As we have noted in the main text, most individual components of SimCLR have appeared in previous work, and the improved performance is a result of a combination of these design choices. Table C.1 provides a high-level comparison of the design choices of our method with those of previous methods. Compared with previous work, our design choices are generally simpler.

In below, we provide an in-depth comparison of our method to the recently proposed contrastive representation learning methods:

DIM/AMDIM (Hjelm et al., 2018; Bachman et al., 2019) achieve global-to-local/local-to-neighbor prediction by predicting the middle layer of ConvNet. The ConvNet is a ResNet that has bewen modified to place significant constraints on the receptive fields of the network (e.g. replacing many 3x3 Convs with 1x1 Convs). In our framework, we decouple the prediction task and encoder architecture, by random cropping (with resizing) and using the final representations of two augmented views for prediction, so we can use standard and more powerful ResNets. Our NT-Xent loss function leverages normalization and temperature to restrict the range of similarity scores, whereas they use a tanh function with regularization. We use a simpler data augmentation policy, while they use FastAutoAugment for their best result.

CPC v1 and v2 (Oord et al., 2018; Hénaff et al., 2019) define the context prediction task using a deterministic strategy to split examples into patches, and a context aggregation network (a PixelCNN) to aggregate these patches. The base encoder network sees only patches, which are considerably smaller than the original image. We decouple the prediction task and the encoder architecture, so we do not require a context aggregation network, and our encoder can look at the images of wider spectrum of resolutions. In addition, we use the NT-Xent loss function, which leverages normalization and temperature, whereas they use an unnormalized cross-entropy-based objective. We use simpler data augmentation.

InstDisc, MoCo, PIRL (Wu et al., 2018; He et al., 2019; Misra & van der Maaten, 2019) generalize the Exemplar approach originally proposed by Dosovitskiy et al. (2014) and leverage an explicit memory bank. We do not use a memory bank; we find that, with a larger batch size, in-batch negative example sampling suffices. We also utilize a nonlinear projection head, and use the representation before the projection head. Although we use similar types of augmentations (e.g., random crop and color distortion), we expect specific parameters may be different.

CMC (Tian et al., 2019) uses a separated network for each view, while we simply use a single network shared for all randomly augmented views. The data augmentation, projection head and loss function are also different. We use larger batch size instead of a memory bank.

Whereas Ye et al. (2019) maximize similarity between augmented and unaugmented copies of the same image, we apply data augmentation symmetrically to both branches of our framework (Figure 2). We also apply a nonlinear projection on the output of base feature network, and use the representation before projection network, whereas Ye et al. (2019) use the linearly projected final hidden vector as the representation. When training with large batch sizes using multiple accelerators, we use global BN to avoid shortcuts that can greatly decrease representation quality.